# Existence and boundary regularity for degenerate phase transitions

## TL;DR

This paper investigates the regularity and existence of solutions for a degenerate phase transition model, establishing boundary continuity and deriving a modulus to quantify it, which aids in proving the existence of physical solutions.

## Contribution

It provides new regularity results for weak solutions of a degenerate two-phase Stefan problem and demonstrates the existence of physically meaningful solutions.

## Key findings

- Weak solutions are continuous up to the boundary.
- A modulus of continuity is derived for these solutions.
- Existence of physical solutions is established.

## Abstract

We study the Cauchy-Dirichlet problem associated to a phase transition modeled upon the degenerate two-phase Stefan problem. We prove that weak solutions are continuous up to the parabolic boundary and quantify the continuity by deriving a modulus. As a byproduct, these a priori regularity results are used to prove the existence of a so-called physical solution.